When new, gain and offset of exhaust gas sensors may be determined in order to calibrate the sensor so that accurate measurements of exhaust gas constituents may be obtained. Over time, however, sensor parameters can drift resulting in measurement error. For example, a sensor gain and offset, which are calibration parameters used to define a linear transformation from sensor output to a measured parameter, may drift during sensor operation. Thus, periodic updates of the sensor parameters, including sensor gain and offset, during the lifetime of the sensor may be used.
One method to calibrate the sensor during its lifetime in a motor vehicle includes measuring gain and offset during a period when the concentration of a desired gas constituent is known, such as deceleration fuel shut off (DFSO) when the exhaust gas may be comprised substantially of ambient air. However, the inventors herein have recognized a problem with this method. Specifically, during DFSO, the gasses in the vicinity of the sensor may not have enough time to reach a steady state (e.g., equilibrium) of ambient conditions as DFSO has a limited duration. In other words, residual exhaust gasses may remain in the vicinity of the sensor following the onset of DFSO due to gas mixing effects, exhaust and/or intake restrictions and cavities, the plurality of strokes comprising a combustion cycle, restrictions of the protective metal housing of the sensor itself, etc. For this reason, it may not be possible to correctly determine gain and offset of the sensor and, therefore, calibrate the sensor to provide accurate readings of exhaust gas constituents.
As such, in one approach, the above issue may be at least partially addressed by projecting an equilibrium value of a desired exhaust gas constituent reading of the exhaust gas sensor, such as during transient DFSO conditions where the sensor is exposed to a mixture of ambient air and exhaust gas. For example, during engine non-fueling conditions such as DFSO, an equilibrium value may be generated based on a trajectory of an exhaust gas constituent reading of the exhaust gas sensor. Specifically, generating the equilibrium value of the exhaust gas constituent reading based on the trajectory may include applying a projection model to a plurality of successive exhaust gas constituent readings taken during the engine non-fueling conditions. In this manner, the equilibrium value of an exhaust gas constituent may be estimated, and thus gain and/or offset of the sensor may be accurately determined, even if gasses in the vicinity of the sensor have not reached a steady state corresponding to ambient air.
It should be understood that the summary above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure.